At this point, I think you will be clear enough on what Deutsch is about to set your own reading agenda, if you hadn’t already. My purpose with this reading guide has not been to discourage you from reading the other parts, but just to make sure you didn’t miss the best stuff. The remaining chapters of The Fabric of Reality are on computation (chapters 5, “Virtual Reality”; 6, “Universality and the Limits of Computation”; and 9, “Quantum Computers”), a fascinating chapter on time travel that relies heavily on the theories of the multiverse and computation (chapter 12, “Time Travel”), more in-depth discussions on the problem of induction and the philosophy of science (chapters 7, “A Conversation About Justification”; and 10, “The Nature of Mathematics”), and the conclusion of his “Theory of Everything”, chapter 13, “The Four Strands” (this one includes an extensive discussion/critique of Thomas Kuhn, in comparison with Popper; I’m not sure he entirely grasps Kuhn’s reasons for writing what he did, but it’s interesting for those familiar with Kuhn nonetheless).
The Beginning of Infinity contains a lot of repetition from and restating of The Fabric of Reality in the service of a new thesis, which you may wish to come to know by just reading straight through, with or without finishing The Fabric of Reality. For individual selections though, I recommend, in addition to chapter 3, chapters 10 and 13 (“A Dream of Socrates” and “Choices”), as they bring the epistemology into the political realm, much as Popper himself did in his most famous single work, The Open Society and its Enemies, changing the question from “how can we ensure we are right?” to “how can we ensure we are governed justly?” Chapter 12, “A Physicists History of Bad Philosophy”, really amps up his polemic about the non-adoption of the multiverse theory.
In addition to the introduction to Popper by Bryan Magee and The Selfish Gene, Deutsch also includes two full works by Popper in his list of essential reading, but together they come to about 800 pages. Like most academic writers, Deutsch vastly over-estimates the average reader’s time, patience, and interest in the topic. The book Popper Selections, edited by David Miller, is a much better way to start in on Popper in his own words for those who are interested. Drawn from his major works anyway, the sections on the theory of knowledge and the philosophy of science are the first two sections and come to only 200 pages, and are easy to understand after reading Deutsch and Magee. I suggest getting your fill of Deutsch first though. (Here are some quotations from Popper I’ve extracted, if you want a taste.)